Sen. Olympia J. Snowe of Maine’s announcement two weeks ago that she won’t seek re-election this year has set off a chaotic last-minute rush by potential candidates to organize campaigns — some from scratch — ahead of a Thursday deadline to qualify to run.

As of Tuesday afternoon, three Republican candidates — and no Democrats — had submitted the necessary 2,000 signatures to state election officials to ensure their name is on the ballot for the June 12 primary elections.

At least two or three Democrats are expected to enter the race, though it’s uncertain what the party’s field will be at 5 p.m. Thursday, when signatures are due for partisan candidates.

Even the three Republican hopefuls — Maine Secretary of State Charles E. Summers Jr., former state Sen. Richard A. Bennett and Scott D’Amboise — only turned in their signatures this week, highlighting the difficulty potential Senate hopefuls have faced in jump-starting their campaigns.

“Two weeks is really not a lot of time to accomplish this,” said Jennifer E. Duffy, who covers Senate races for the Cook Political Report. “They’re scrambling on both sides.”

Nonpartisan candidates have until June 1 to submit 4,000 signatures to qualify, giving breathing room to former Gov. Angus King, who has said he will run as an independent.

Mr. King, a popular governor from 1995 to 2003 who had a reputation for rising above the partisan fray, would be the race’s favorite, many political specialists say.

“It’s his race to lose,” said Kenneth Palmer, a political science professor emeritus at University of Maine.

But Mr. Palmer quickly added that without knowing the full field, the race is “way too fluid to make any calls.”

Mr. King hasn’t said which party he would caucus with if elected, even hinting he would caucus with neither, although there is speculation the moderate former governor would side with Democrats.

John Baldacci, who succeeded Mr. King as governor, has been mentioned as a possible Democratic candidate. Like Mr. King he served eight years as governor and was popular with voters.

Democratic U.S. Rep. Chellie Pingree had considered vying for Mrs. Snowe’s seat but decided last week to seek re-election in her Portland-area district.